With her Irish setter hair, invisible goatee beard, Popeye arms and a trace of a decaf limey accent, Madonna is back with her stately new film vehicle, The Next Best Thing - which turns out to double, exasperatingly, as a feature-length promo-showcase for her cover version of American Pie.

Dismayingly queenly, and pervasively, subtly humourless and unrelaxed, Madonna plays Abbie, a yoga instructor in LA. Abbie's job is funkily to instruct her various classes, and there's even a scene in which, broodingly alone, she does a very complicated black-belt yoga manoeuvre involving lots of tricky supple things, although this is filmed in long shot. Abbie is smart, funny and has what her outgoing boyfriend crisply informs us is a "fantastic body". Yet she can't find a man and yearns for a baby.

As fortune would have it, she is best friends with Robert (Rupert Everett), a designer gardener, gay, recently jilted. They are lonely; a one-night-only sexual chemistry sparks between the two of them; Abbie gets pregnant. And so a thoroughly modern Millie, 21st-century solution suggests itself: they will set up house together; Robert will be a father to the child - but they can both date as if she was a single mom, and he her gay buddy, sharing house.

It's a seductively contemporary-sounding ménage, a witty fictional response to the Blairite/Clintonite quasi-liberal politics of upholding family values while at the same time trying to redefine the "family". It appears to challenge assumptions from all sides of the sexual politics spectrum; and as gay men might tire of the hedonistic stereotype, so straight men might feel envious of what appears to be gay men's unmediated access to female friendship. (Tina Brown's Talk magazine recently suggested that women desire emotionally intelligent men who are JGE - Just Gay Enough.)

It's not an entirely new idea, though: as recently as 1998, Nicholas Hytner's The Object of My Affection had a very similar high concept, and as for the idea of a gay man having intensely loving feelings for his children within a conventional marital household, there is the example of Oscar Wilde - which, oddly, is never invoked in this film.

But what lets it down from the word go - what sinks this film with all hands - is the relentlessly heavy-handed feel to the whole enterprise. John Schlesinger directs with granite gloves. Effectively, Rupert Everett is being asked to reprise and extend his grandstanding performance in My Best Friend's Wedding, complete with rapid-response cellphone advice, mercurial wit, playacting, singing in public, etc etc.

But where that performance had lightness and insouciant style, his screen presence here is freighted with brow-furrowing earnestness and moments in which Everett has to break down in tears and - inevitably - come to terms with his own father. Finally, Abbie and Robert's household falls apart on the question of who gets the child when a relationship of Abbie's gets serious, and Rupert finds himself in a very self-conscious new version of Kramer Vs Kramer, with Everett as a taller, handsomer and better dressed Dustin Hoffman.

The family courts in the state of California, are represented, I sense accurately, as pretty reactionary in the matter of gays and childcare: for a reversal of roles, it's interesting to consider Mike Newell's The Good Father from 1987, which had Anthony Hopkins as a man inciting his friend, played by Jim Broadbent, to contest his estranged wife's and her female lover's application for child custody. In the time of Kramer and The Good Father, gay politics and gender politics could be a bitter and acrimonious bone of contention between the principals themselves; here, a heavy consensus notionally reigns and that kind of high-octane opposition is off the agenda, leaving only a squishy, touchy-feely sense of sadness.

None of this need have been a problem, had it not been that Madonna never fully inhabits her role, never for one moment forgets her mission to attain seriousness and maturity in a new medium - yet clearly considers it expedient to keep in touch with her music fan base. (At one point she says allusively: "I've made up my mind, and I'm having this baby.")

Madonna gives an averagely competent account of herself, yet the magic ingredient of believable spontaneity and fun is missing from the first half of the film, and absent from the second half are the real anger and real pain that go with the end of all relationships.